Torsional mode quartz crystal device

ABSTRACT

The disclosed technology generally relates to quartz crystal devices and more particularly to quartz crystal devices configured to vibrate in torsional mode. In one aspect, a quartz crystal device configured for temperature sensing comprises a fork-shaped quartz crystal comprising a pair of elongate tines laterally extending from a base region in a horizontal lengthwise direction of the fork-shaped quartz crystal. Each of the tines has formed on one or both of opposing sides thereof a vertically protruding line structure laterally elongated in the horizontal lengthwise direction. The quartz crystal device further comprises a first electrode and a second electrode formed on the one or both of the opposing sides of each of the tines and configured such that, when an electrical bias is applied between the first and second electrodes, the fork-shaped quartz crystal vibrates in a torsional mode in which each of the tines twists about a respective axis extending in the horizontal lengthwise direction.

INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS

Any and all applications for which a priority claim is identified in theApplication Data Sheet as filed with the present application are herebyincorporated by reference under 37 CFR 1.57.

This application is a continuation of U.S. patent application Ser. No.17/305,898, filed Jul. 16, 2021, which is a continuation of U.S. patentapplication Ser. No. 16/548,675, filed Aug. 22, 2019, now U.S. Pat. No.11,070,191, the contents of which are hereby expressly incorporated byreference in their entireties.

BACKGROUND Field

The disclosed technology generally relates to quartz crystal devices andmore particularly to quartz crystal devices configured to vibrate intorsional mode.

Description of the Related Art

A crystal oscillator is an electronic oscillator circuit that uses themechanical resonance of a vibrating crystal of piezoelectric material tocreate an electrical signal with a precise frequency. This frequency canprovide a stable reference signal, e.g., a clock signal, for digitalintegrated circuits, and to stabilize frequencies for radio transmittersand receivers. One type of piezoelectric resonator used is quartzcrystal, and oscillator circuits using the quartz crystal are referredto as quartz crystal oscillators.

A quartz crystal oscillator vibrates at a stable frequency by beingdistorted by an electric field when voltage is applied to an electrodenear or on the crystal. This property is known as electrostriction orinverse piezoelectricity. When the field is removed, the quartz, whichoscillates in a precise frequency, generates an electric field as itreturns to its previous shape, which in turn can generate a voltage.This characteristic of a quartz crystal can be modeled as an RLCcircuit. Advantages of quartz crystal oscillators include frequencyaccuracy, stability, and low power consumption. Because of theseadvantages, quartz crystal oscillators are used in many consumer devicessuch as wristwatches, clocks, radios, computers and cellphones, to namea few. Quartz crystals are also found inside test and measurementequipment, such as counters, signal generators, and oscilloscopes.However, high reliability is needed to fully benefit from the advantagesof the quartz crystal oscillators.

SUMMARY

In one aspect, a quartz crystal device configured for temperaturesensing comprises a fork-shaped quartz crystal comprising a pair ofelongate tines laterally extending from a base region in a horizontallengthwise direction of the fork-shaped quartz crystal. Each of thetines has formed on one or both of opposing sides thereof a verticallyprotruding line structure laterally elongated in the horizontallengthwise direction. The quartz crystal device further comprises afirst electrode and a second electrode formed on the one or both of theopposing sides of each of the tines and configured such that, when abias is applied between the first and second electrodes, the fork-shapedquartz crystal vibrates in a torsional mode in which each of the tinestwists about a respective axis extending in the horizontal lengthwisedirection.

In another aspect, a quartz crystal device configured for temperaturesensing comprises a fork-shaped quartz crystal comprising a pair ofelongate tines laterally extending from a base region in a horizontallengthwise direction of the fork-shaped quartz crystal. The quartzcrystal device further comprises a first electrode and a secondelectrode formed on the one or both of the opposing sides of each of thetines. Each of the first and second electrodes have surfaces facing eachother in a widthwise direction of the fork-shaped quartz crystal andconfigured such that, when a bias is applied between the first andsecond electrodes, the fork-shaped quartz crystal vibrates in atorsional mode in which each of the tines twists about a respective axisextending in the horizontal lengthwise direction.

In yet another aspect, a quartz crystal oscillator device configured fortemperature sensing comprises a quartz crystal device bonded to apackage substrate. The quartz crystal device comprises a fork-shapedquartz crystal device comprising a pair of elongate tines laterallyextending from a base region in a horizontal lengthwise direction of thefork-shaped quartz crystal, wherein each of the tines has formed on oneor both of opposing sides thereof a vertically protruding line structurelaterally elongated in the horizontal lengthwise direction andelectrodes configured such that the fork-shaped quartz crystal vibratesin a torsional mode in which each of the tines twists about an axisextending in the horizontal lengthwise direction. The quartz crystaloscillator device further comprises an integrated circuit (IC) dieelectrically connected to the quartz crystal device and bonded to thepackage substrate.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A schematically illustrates a plan view of a main surface of afork-shaped torsional mode quartz crystal device.

FIG. 1B schematically illustrates a cross-sectional view of thefork-shaped torsional mode quartz crystal device illustrated in FIG. 1A,including a schematic electric field path.

FIG. 2A schematically illustrates a perspective view of the fork-shapedtorsional mode quartz crystal device illustrated in FIGS. 1A and 1B.

FIG. 2B schematically illustrates a perspective view of the fork-shapedtorsional mode quartz crystal device illustrated in FIG. 2A, in whichthe tines are twisted and displaced in operation under a bias.

FIG. 3 illustrates a circuit representation of a quartz crystal device.

FIG. 4 is a graph illustrating motional resistance and motionalcapacitance as a function of a crystal thickness for the fork-shapedtorsional mode quartz crystal device illustrated in FIGS. 1A and 1B.

FIG. 5A schematically illustrates a plan view of a first main (top)surface of a fork-shaped torsional mode quartz crystal device comprisinga mesa structure, according to embodiments.

FIG. 5B schematically illustrates a plan view of a second main (bottom)surface of the fork-shaped torsional mode quartz crystal deviceillustrated in FIG. 5A.

FIG. 5C schematically illustrates a cross-sectional view of thefork-shaped torsional mode quartz crystal device illustrated in FIGS. 5Aand 5B at tip regions of the tines.

FIG. 5D schematically illustrates a cross-sectional view of thefork-shaped torsional mode quartz crystal device illustrated in FIGS. 5Aand 5B at midsections of the tines.

FIG. 5E schematically illustrates a cross-sectional view of thefork-shaped torsional mode quartz crystal device illustrated in FIGS. 5Aand 5B at a base region.

FIG. 6A schematically illustrates a perspective view of the fork-shapedtorsional mode quartz crystal device illustrated in FIGS. 5A-5E.

FIG. 6B schematically illustrates a cross-sectional view of thefork-shaped torsional mode quartz crystal device illustrated in FIG. 6A.

FIG. 6C schematically illustrates a perspective view of the fork-shapedtorsional mode quartz crystal device illustrated in FIGS. 6A-6B, inwhich the tines are twisted in operation under a bias.

FIG. 7 schematically illustrates different crystal cuts and orientationsfor different types of quartz crystal devices including a fork-shapedtorsional mode quartz crystal device, according to embodiments.

FIG. 8A illustrates a simulation of a linear temperature coefficient ofa fork-shaped torsional mode quartz crystal device as a function of anangle of tilt θ relative to the X-axis of a quartz crystal, according toembodiments.

FIG. 8B illustrates a simulated frequency versus temperature curve of afork-shaped torsional mode quartz crystal device at an angle of tilt of−30° relative to the X-axis of a quartz crystal, according toembodiments.

FIG. 8C illustrates a simulated frequency versus temperature curve of afork-shaped torsional mode quartz crystal device at an angle of tilt of30° relative to the X-axis of a quartz crystal, according toembodiments.

FIG. 9 illustrates simulated frequency versus thickness for fork-shapedtorsional mode quartz crystal devices with and without a mesa structure.

FIG. 10A is a graph illustrating simulated motional resistance as afunction of frequency for fork-shaped torsional mode quartz crystaldevices with and without a mesa structure.

FIG. 10B is a graph illustrating simulated motional capacitance as afunction of frequency for fork-shaped torsional mode quartz crystaldevices with and without a mesa structure.

FIG. 10C is a graph illustrating a simulated quality factor as afunction of frequency for fork-shaped torsional mode quartz crystaldevices with and without a mesa structure.

FIG. 11 is a graph illustrating simulated frequency and motionalcapacitance as a function of mesa thickness for a fork-shaped torsionalmode quartz crystal device, according to embodiments.

FIG. 12A is a graph illustrating simulated motional resistance andmotional capacitance as a function of a ratio of thicknesses between aline region and a recessed region of a tine for a fork-shaped torsionalmode quartz crystal device comprising a mesa structure, according toembodiments.

FIG. 12B is a graph illustrating simulated frequency and quality factoras a function of a ratio of thicknesses between a line region and arecessed region of a tine for a fork-shaped quartz crystal devicecomprising a mesa structure, according to embodiments.

FIG. 13A is a graph illustrating simulated motional resistance andmotional capacitance as a function of a ratio between a width of a lineregion and a tine width for a fork-shaped quartz crystal devicecomprising a mesa structure, according to embodiments.

FIG. 13B is a graph illustrating simulated frequency and quality factoras a function of a ratio of between a width of a line region and a tinewidth for fork-shaped torsional mode quartz crystal device comprising amesa structure, according to embodiments.

FIG. 14A is a graph illustrating simulated motional resistance andmotional capacitance as a function of a ratio between a length of a tipregion of a tine excluding the line region a length of the tineincluding the line region for a fork-shaped torsional mode quartzcrystal device comprising a mesa structure, according to embodiments.

FIG. 14B is a graph illustrating simulated frequency and quality factoras a function of a ratio between a length of a tip region of a tineexcluding the line region a length of the tine including the line regionfor a fork-shaped torsional mode quartz crystal device comprising a mesastructure, according to embodiments.

FIG. 15A illustrates experimentally measured frequency and motionalcapacitance versus mesa thickness for a fork-shaped torsional modequartz crystal device comprising a mesa structure, according toembodiments.

FIG. 15B illustrates an experimentally measured frequency versustemperature curve for a fork-shaped torsional mode quartz crystal devicecomprising a mesa structure, according to embodiments.

FIG. 16A illustrates a plan-view of a fork-shaped quartz crystal devicecomprising a mesa structure packaged in a ceramic package substrate,according to embodiments.

FIG. 16B illustrates a cross-sectional view of the packaged fork-shapedquartz crystal device illustrated in FIG. 16A.

FIG. 17A illustrates a plan-view of a quartz crystal oscillator devicecomprising a fork-shaped quartz crystal device packaged in a ceramicpackage substrate, according to embodiments.

FIG. 17B illustrates a cross-sectional view of the packaged quartzcrystal oscillator device illustrated in FIG. 17A.

FIG. 18A schematically illustrates a plan view of a main (top) surfaceof a fork-shaped torsional mode quartz crystal device comprising a mesastructure and vibration isolation arms, according to embodiments.

FIG. 18B schematically illustrates a cross-sectional view of thefork-shaped torsional mode quartz crystal device illustrated in FIG. 18Aat tip regions of the tines.

FIG. 18C schematically illustrates a cross-sectional view of thefork-shaped torsional mode quartz crystal device illustrated in FIG. 18Aat a midsection of the tines and tip regions of the vibration isolationarms.

FIG. 19A illustrates a plan-view of a quartz crystal oscillator devicecomprising a fork-shaped quartz crystal device packaged in a ceramicpackage substrate, according to embodiments.

FIG. 19B illustrates a cross-sectional view of the packaged quartzcrystal oscillator device illustrated in FIG. 19A.

DETAILED DESCRIPTION

The following detailed description is now directed to certain specificembodiments of the disclosure. In this description, reference is made tothe drawings wherein like parts are designated with like numeralsthroughout the description and the drawings.

In the following, various embodiments of quartz crystal devices andquartz crystal oscillator devices are disclosed. In particular, thedisclosed quartz crystal devices comprise a fork-shaped or tuningfork-shaped quartz crystal that is configured to vibrate in a torsionalmode and/or operate as a temperature sensor. Advantageously, the quartzcrystal devices are designed such that its vibrating frequency is bothextremely sensitive to temperature and highly linear. The highsensitivity offers the ability to detect fine changes in temperature,where the degree of sensitivity can be tailored depending on variousimplementations disclosed herein. Further, a frequency-based techniquehas the advantage of being immune to amplitude noise in the measurementsystem, which is a feature not present in other types of temperaturesensors such as a thermocouple, a thermistor, or resistance temperaturedetectors (RTDs). Furthermore, the disclosed fork-shaped quartz crystaldevices can enable remote temperature sensing by using an antenna topick up the frequency of the electromagnetic waves emitted by thefork-shaped quartz crystal device.

In various examples disclosed herein, a quartz crystal device configuredfor temperature sensing comprises a fork-shaped quartz crystalcomprising a base region and a pair of elongate tines laterallyextending from the base region in a lengthwise direction. The quartzcrystal additionally comprises a first electrode and a second electrodeformed on the one or both of opposing sides of each of the tines andconfigured such that, when a bias is applied between the first andsecond electrodes, the fork-shaped quartz crystal vibrates in atorsional mode in which each of the tines twists about an axis extendingin the lengthwise direction.

FIG. 1A schematically illustrates a plan view of an example fork-shapedtorsional mode quartz crystal device 100. FIG. 1B schematically across-sectional view of the fork-shaped torsional mode quartz crystaldevice illustrated in FIG. 1A. The quartz crystal device 100 comprises abase 112, a first or left tine 114 projecting from the base 112 andextending generally along a lengthwise direction, e.g., x-axis. Thefork-shaped quartz crystal device 100 additionally comprises a second orright tine 116 or prong projecting from the base 112 and extendinggenerally along the same lengthwise direction. The tines can also bereferred as arms or prongs. The first tine 114 and second tine 116 canbe generally parallel to one another. In various quartz crystal devicesdisclosed herein, electrodes are formed on various surfaces thereof suchthat the tines are configured to vibrate at least in a torsional mode,as described below.

The base 112 supporting the first and second tines 114, 116 can includemultiple portions. For example, in the illustrated example, the base 112comprises a first or upper base portion 112A from which the first andsecond tines 114, 116 immediately extend and a second or lower baseportion 112B forming a terminal portion of the quartz crystal device100. The first and second base portions 112A, 112B can be defined by afirst and second width, respectively. The second base portion 112B canbe configured such that the fork-shaped torsional mode quartz crystaldevice 100 can be mounted to a ceramic package or other supportstructures. In the illustrated example, the second base portion 112Bconfigured for mounting on a ceramic package is wider than the firstbase portion 112A connected to the first and second tines 114, 116. Suchconfiguration can reduce the amount of vibration leakage from the firstand second tines 114, 116 to the base 112, such that the fork-shapedtorsional mode quartz crystal device 100 vibrates with increasedefficiency. However, embodiments are not so limited and the firstportion 112A can have the same or larger width than that of the secondbase portion 112B.

The fork-shaped torsional mode quartz crystal device 100 has varioussurfaces having formed thereon electrode patterns that are collectivelyadapted for vibration of the quartz crystal device 100 in a torsionalmode. Referring to FIG. 1A, quartz crystal device 100 shows on a firstor front side 118 (FIG. 1B) a first main surface, e.g., a front surface.The electrode patterns on the first main surface include a firstelectrode pattern 124 of a first polarity, e.g., one of a negative orpositive electrode pattern, and a second electrode pattern 128 of asecond polarity, e.g., the other of the negative or positive electrodepattern. While not illustrated, the fork-shaped torsional mode quartzcrystal device 100 also has on a second or rear side 120 opposite thefirst or front side 118 a second main surface, e.g., a back surface. Thesecond main surface back surface also includes various portions of thefirst electrode pattern 124′ and the second electrode pattern 128′formed thereon. As described herein and throughout the specification, itwill be understood that, while electrode patterns labeled with differentreference numerals, e.g., first electrode patterns 124 and 124′, may beformed on different surfaces, they may be electrically connected to eachother and therefore be at the same potential.

As described herein and throughout the specification, relative positionsof various features formed on a side of a quartz crystal device, e.g.,the first electrode patterns 124, 124′ and second electrode patterns128, 128′, may be described as viewed from the respective sides. Assuch, it will be appreciated that positions that are described as havingopposite lateral positions, when disposed on opposing sides, may bereferring to the same physical position. For example, in FIG. 1A, whenviewed from the first side 118, the first and second tines 114, 116 arepositioned on left and right relative positions, respectively, whilewhen viewed from the second side 120 (FIG. 1B), the first and secondtines 114, 116 would be positioned on right and left relative positions,respectively.

Referring to the plan view illustrated in FIG. 1A, viewed from the firstside 118, the first (e.g., negative) electrode pattern 124 formed on thetop surface includes first to fourth first electrode portions 124A-124D,and the second (e.g., positive) electrode pattern 128 formed on the topsurface includes first to fourth second electrode portions 128A-128D.The first electrode pattern 124 includes a first portion 124A covering afirst (right) side of the base 112 and extends upward therefrom in thex-direction in the form of the second thin strip portion 124B along aright or outer edge portion of the second tine 116, and terminatesadjacent to the third portion 128C of the second electrode pattern 128formed on the terminal end portion of the second tine 116. The firstelectrode pattern 124 additionally includes the third portion 124Cformed on the terminal end portion of the first tine 114, extendsdownward therefrom in the x-direction in the form of the fourth thinstrip portion 124D along a left or outer edge portion of the first tine114, and terminates adjacent to the first portion 128A of the secondelectrode pattern 128 formed on the second (left) side of the base 112.

Still referring to the plan view illustrated in FIG. 1A, the secondelectrode pattern 128 formed on the top surface includes the firstportion 128A covering a second (left side) of the base 112 and extendsupward therefrom in the x-direction and forks or splits into the secondthin strip portion 128B formed and extending upward along a left orinner edge portion of the second tine 116, and a fourth thin stripportion 128D formed along and extending upward along a right or inneredge portion of the first tine 114. The fourth thin strip portion 128Dterminates adjacent to the third portion 124C of the first electrodepattern 124 formed on the terminal end of the first tine 114. The secondthin strip portion 128B extends to connect to the third portion 128C ofthe second electrode pattern 128 formed on the terminal end portion ofthe second tine 116.

While not illustrated, the combination of the first and second electrodepatterns 124′, 128′ formed on the rear side 120 may generally be shapedsimilarly as the combined pattern of the first and second electrodepatterns 124, 128 formed on the front side 118 as described above,except that their polarities are interchanged. The first (e.g.,negative) electrode pattern 124′ formed on the bottom surface includesfirst to fourth portions 124A′-124D′, and the second (e.g., positive)electrode pattern 128′ formed on the bottom surface includes first tofourth portions 128A′-128D′. The second electrode pattern 128′ includesa first portion 128A′ covering a first (right side) of the base 112 andextends upward therefrom in the x-direction in the form of the secondthin strip portion 128B′ along a right or outer edge portion of thefirst tine 114, and terminates adjacent to the third portion 124C′ ofthe first electrode pattern 124′ formed on the terminal end portion ofthe first tine 114. In addition, the second electrode pattern 128′includes the third portion 128C′ formed on the terminal end portion ofthe second tine 116, extends downward therefrom in the x-direction inthe form of the fourth thin strip portion 128D′ along a left or outeredge portion of the second tine 116, and terminates adjacent to thefirst portion 124A′ of the first electrode pattern 124′ formed on thesecond (left) side of the base 112 when viewed from the rear side 120.

Additionally, the first electrode pattern 124′ formed on the bottomsurface (not shown) includes the first portion 124A′ covering a second(left side) of the base 112 and extends upward therefrom in thex-direction and forks or splits into the second thin strip portion 124B′formed and extending upward along a left or inner edge portion of thefirst tine 114, and a fourth thin strip portion 124D′ formed along andextending upward along a right or inner edge portion of the second tine116. The fourth thin strip portion 124D′ terminates adjacent to thethird portion 128C′ of the second electrode pattern 128′ formed on theterminal end of the second tine 116. The second thin strip portion 124B′extends to connect to the third portion 124C′ of the first electrodepattern 124′ formed on the terminal end portion of the first tine 114.

As described above, various portions of the first electrode pattern 124on the first side 118 and the first electrode pattern 124′ on the secondside 120 are electrically connected to each other. Similarly, variousportions of the second electrode pattern 128 on the first side 118 andthe second electrode pattern 128′ on the second side 120 areelectrically connected to each other. The resulting relative positionsof different portions of the first electrode patterns 124, 124′ and thesecond electrode patterns 128, 128′ in a cross-sectional view areillustrated in FIG. 1B. FIG. 1B schematically illustrates across-sectional view of the fork-shaped torsional mode quartz crystaldevice 100 through the section A-A illustrated in FIG. 1A. Thecross-sectional view of the first tine 114 shows a first main surface onthe first side 118 having the fourth strip portion 124D of the firstelectrode pattern 124 formed on the outer edge portion thereof, and thefourth strip portion 128D of the second electrode pattern 128 formed onthe inner edge portion thereof. On the other hand, a second main surfaceon the second side 120 has the second strip portion 124B′ of the firstelectrode pattern 124′ formed on the inner edge portion of the firsttine 114, and the second strip portion 128B′ of the second electrodepattern 128′ formed on the outer edge portion of the first tine 114. Thesection A-A additionally illustrates a cross-sectional view of thesecond tine 116 showing a first main surface of the first side 118having the second strip portion 124B of the first electrode pattern 124formed on the outer edge portion thereof, and the second strip portion128D of the second electrode pattern 128 formed on the inner edgeportion thereof. On the other hand, the second main surface of thesecond side 120 has the fourth strip portion 124D′ of the firstelectrode pattern 124′ formed on the inner edge portion of the secondtine 116, and the fourth strip portion 128D′ of the second electrodepattern 128′ formed on the outer edge portion of the second tine 116.

In operation, electrical pulses having a first (e.g., one of negative orpositive) polarity may be applied to the first electrode patterns 124,124′ (including the second and fourth strip portions 124B, 124D on thefront main surfaces of the second and first tines 116, 114,respectively, and the second and fourth strip portions 124B′, 124D′ onthe back main surfaces of the first and second tines 116, 114,respectively, as illustrated in FIG. 1B). On the other hand, electricalpulses having a second (e.g., the other of negative or positive)polarity may be applied to the second electrode patterns 128, 128′(including the second and fourth strip portions 128B, 128D on the frontmain surfaces of the second and first tines 116, 114, respectively, andto the second and fourth strip portions 128B′, 128D′ on the back mainsurfaces of the first and second tines 114, 116, respectively, asillustrated in FIG. 1B). It will be appreciated that, as disclosedherein and throughout the specification, positive and negativepolarities may describe relative polarities, such that voltages thathave the same sign but different magnitudes may be described as havingpositive and negative polarities. While embodiments are not so limited,pulses having the first and second polarities may be applied to thequartz crystal device 100 simultaneously.

Still referring to FIG. 1B. when the first and second electrode patterns124/124′, 128/128′ are biased as described herein, the resultingelectric field generally follows, e.g., on average, the curvilinearpaths indicated by the arrows, from the second strip portion 128B on thefront surface of the second tine 116, the fourth strip portion 128D onthe front surface of the first tine 114, the second strip portion 128B′on the back surface of the first tine 114 and the fourth strip portion128D′ on the back surface of the second tine 116, to the second stripportion 124B on the front surface of the second tine 116, the fourthstrip portion 124D on the front surface of the first tine 114, thesecond strip portion 124B′ on the back surface of the first tine 114 andthe fourth strip portion 124D′ on the back surface of the second tine116, respectively.

FIGS. 2A and 2B schematically illustrate perspective views of thefork-shaped torsional mode quartz crystal device 100 described abovewith respect to FIGS. 1A and 1B. FIG. 2A illustrates the quartz crystaldevice 100 in a rest state, while FIG. 2B illustrates a fork-shapedtorsional mode quartz crystal device 100 under a bias. When the firstand second electrode patterns 124, 128 are subjected to negative andpositive relative voltages, respectively, as described above, such thatthe electric field lines are directed from various portions of thesecond electrode patterns 128, 128′ to corresponding portions of thefirst electrode patterns 124, 124′ in a manner as described above, thefirst and second tines 114, 116 twist about the x-axis (FIG. 1A)extending in the lengthwise direction, as illustrated in FIG. 2B. Whenthe first and second electrode patterns 124, 128 are subjected to pulsednegative and positive voltages, the quartz crystal device 100 can togglebetween the rest state illustrated in FIG. 2A and the deformed stateillustrated in FIG. 2B.

FIG. 3 illustrates an equivalent circuit representation of quartzcrystal oscillators. The equivalent circuit representation illustratedin FIG. 3 is sometimes referred to as Butterworth Van Dyke (BVD)equivalent circuit. Without being bound to any theory, the electricalbehavior of a piezoelectric bulk oscillator, such as a quartz crystaldevice near the vicinity of its frequencies of resonance can berepresented by the equivalent circuit 300. The equivalent circuit 300includes two parallel paths between terminal nodes. The first pathincludes a static capacitance (C₀) which can represent a electrodecapacitance of the quartz crystal device. The second path includes amotional inductor (L₁), a motional capacitor (C₁) and a motionalresistor (R₁), and may sometimes be referred to as the motional arm. TheL₁, C₁ and R₁ and can be associated with the inertia, stiffness andinternal losses of the mechanical vibrating system, respectively.

A quality factor (Q) can be used to benchmark quartz crystal resonance.The Q factor can represent a ratio of energy stored versus energydissipated in a vibration cycle. Higher Q factors are generallyassociated with higher frequency stability and accuracy of a quartzcrystal device. The magnitude of the Q factor can be associated with thequalitative behavior of a quartz crystal device. Without loss ofgenerality, for example, a system with a very low Q factor can be anoverdamped system. Below a certain value of the Q factor, an overdampedsystem may not oscillate at all.

Without being bound to any theory, the Q factor of a quartz crystaldevice can sometimes be expressed by the following expression:

$\begin{matrix}{Q = \frac{1}{2\pi f_{s}R_{1}C_{1}}} & \lbrack 1\rbrack\end{matrix}$

In equation [1], f_(s) is the series resonance frequency, and theproduct of R₁ and C₁ is sometimes referred to as a motional timeconstant τ, which can vary, among other things, with the angle of cutand the mode of vibration. According to Eq. [1], a larger R₁ results ina lower Q. Thus, a relatively large value of C₁ may be desired for theoperating resonance of a piezoelectric device.

Without being bound to any theory, a quartz crystal device such as thequartz crystal device 100 described above with respect to FIGS. 1A-1Band 2A-2B vibrating in a torsional vibrational mode can have a quartzcrystal frequency f that can be approximated by the following equation:

$\begin{matrix}{f \approx {k\frac{t}{lw}}} & \lbrack 2\rbrack\end{matrix}$

In equation [2], k is a constant for a given geometry and cut angle ofthe quartz crystal, l or L represents the tine length, w or W representsthe tine width and t represents the tine thickness.

Various applications increasingly demand quartz crystal devices to beminiaturized. To fit a quartz crystal device into a miniature package,the size of the quartz crystal device may be correspondingly scaled. Asindicated by Eq. [2] above, for a constant width (W), to keep thefrequency a constant, the tine length (L) and crystal thickness (t) maybe scaled simultaneously.

FIG. 4 illustrates a graph plotting experimental crystal parameters (R₁and C₁) obtained as function of crystal thickness (t), from a quartzcrystal device such as the fork-shaped torsional mode quartz crystaldevice 100 described above with respect to FIGS. 1A-1B and 2A-2B. Thegraph of FIG. 4 was obtained from a quartz crystal device vibrating in atorsional mode crystal packaged in 5.0 mm×1.8 mm ceramic package. Asillustrated, the motional capacitance (C₁) increases substantiallylinearly with increasing crystal thickness (t). On the other hand, themotional resistance (R₁) decreases super-linearly with increasingcrystal thickness (t). For example, as illustrated, R₁ can increase fromabout 30 kΩ to about 100 kΩ when the thickness is reduced from about 75μm to about 50 μm. When the R₁ is too high, the quartz crystal devicecan display unstable frequency and can even stop oscillation. Accordingto various embodiments described herein, quartz crystal devices havingstructures with reduced R₁ are adapted for miniaturization of packagedquartz crystal devices.

To address these and other needs, according to various embodiments, afork-shaped torsional mode quartz crystal device configured fortemperature sensing comprises a fork-shaped quartz crystal comprising abase and a pair of elongate tines laterally extending from the base in alengthwise direction, where each of the tines has formed on one or bothof opposing sides thereof a mesa structure. The mesa structure includesa line structure laterally elongated in the lengthwise direction. Theline structure vertically protrudes above adjacent recessed surfaces andhas sidewalls abutting the recessed surfaces. The quartz crystaladditionally comprises a first electrode and a second electrode formedon the one or both of the opposing sides of each of the tines andconfigured such that the fork-shaped quartz crystal vibrates in atorsional mode. In particular, each of the first and second electrodeshave surfaces facing each other in a widthwise direction of thefork-shaped quartz crystal and configured such that, when a bias isapplied between the first and second electrodes, the fork-shaped quartzcrystal vibrates in a torsional mode in which each of the tines twistsabout an axis extending in the lengthwise direction.

FIGS. 5A-5E schematically illustrate various views of a fork-shapedtorsional mode quartz crystal device 500 comprising a mesa structure,according to embodiments. The quartz crystal device 500 has on a firstor front side 518 (FIGS. 5A, 5C-E) having a first or front main surface,and a second or rear side 520 (FIGS. 5B, 5C-5E) opposite the first orfront side having a second or rear main surface. FIGS. 5A and 5Billustrate a first or front side and a second side or bottom side of thefork-shaped quartz crystal device 500, respectively. FIGS. 5C, 5D and 5Eillustrate cross-sectional views of the quartz crystal device 500 takenat cross-sections B-B, C-C, and D-D, respectively, as illustrated inFIG. 5A. Some features of the fork-shaped quartz crystal device 500comprising a mesa structure are similar to corresponding features of thefork-shaped quartz crystal device 100 without a mesa structure describedabove with respect to FIGS. 1A-1B, and a detailed description of some ofthe similarities may not be repeated herein for brevity.

In a similar manner as described above with respect to FIGS. 1A and 1B,the fork-shaped quartz crystal device 500 comprises a fork-shaped quartzcrystal comprising a base 512, a first tine 514 projecting from the base512 and extending generally along a lengthwise direction, e.g., x-axis,and a second tine 516 projecting from the base 512 and extendinggenerally along the same lengthwise direction. The tines can also bereferred as arms or prongs. The first tine 514 and the second tine 516can be generally parallel to one another. In the illustratedconfiguration, either or both of the first and second tines 514, 516have a substantially uniform width along respective lengths. However,embodiments are not limited and in other configurations, one or both ofthe first and second tines 514, 516 can have uneven or non-uniformwidths along the respective lengths. For example, without limitation,either or both of the first and second tines 514, 516 can be configuredsuch that some portions of the first and/or second tines 514, 516 arewider than some other portions thereof, or such that some portionsdefine a linear, curved, or other suitable shaped tapering width alongthe respective lengths. In various configurations, the centerlines ofthe first and second tines 514, 516 can be generally parallel to eachanother or generally follow parallel paths. While in the illustratedconfiguration, the quartz crystal device 500 has a pair of tines 514,516, embodiments are not so limited and in some other configurations,any of the quartz crystal devices disclosed herein can have a fewer orgreater number of tines projecting from the base 512. For example, insome configurations, without limitations, any of the quartz crystaldevices disclosed herein can have four or more tines projecting from thebase, where any number of the tines are configured to vibrate at leastin a torsional mode.

Still referring to FIGS. 5A and 5B, the base 512 supporting the firstand second tines 514, 516 can include multiple portions or regions. Forexample, in the illustrated example, the base 512 comprises a first baseportion 512A from which the first and second tines 514, 516 directlyextend, and a second base portion 512B that forms an end portion of thefork-shaped quartz crystal device 500. In the illustrated embodiment,the first and second base portions 512A, 512B have the same or similarwidths. However, embodiments are not so limited, and in some otherembodiments, the first and second base portions 512A, 512B can bedefined by different widths. The second base portion 512B can beconfigured such that the quartz crystal device 500 can be mounted to aceramic package or other support structures.

In the illustrated embodiment, a pair of notches, slots or indentations532 recessed inward from opposing side surfaces of the quartz crystaldevice 500. According to embodiments, when present, the notches 532 canreduce the amount of vibration leakage from the first and second tines514, 516 to the base 512, thereby increasing the efficiency of thefork-shaped quartz crystal device 500. In the illustrated embodiment,the notches 532 are formed at an adjoining region between the first andsecond base portions 512A, 512B. However, embodiments are not so limitedand in other embodiments, the notches 532 can be positioned verticallyanywhere between the connected ends of the first and second tines 514,516 and the terminal edge of the base 512. The notches 532 can have anysuitable shape including any polygonal (e.g., rectangular, triangular)or curved (e.g., semicircular, elliptical) shapes.

Referring to FIGS. 5A/5B and 5C, the B-B cross-section illustrates thateach of the first and second tines 514, 516 comprises a tip portion thatgenerally forms a rectangular shape, in a similar manner as the quartzcrystal device 100 described above with respect to FIGS. 1A and 1B. Asillustrated in FIG. 5C, the first and second main surfaces on first andsecond sides 518, 520, respectively, of the fork-shaped quartz crystaldevice 500 at the tip portions of the first and second tines 514, 516can be generally parallel, opposing planar surfaces that are connectedby side surfaces thereof.

Referring to FIGS. 5A/5B and 5D, the C-C cross-section illustrates that,unlike the quartz crystal device 100 described above with respect toFIGS. lA and 1B, each of the first and second tines 514, 516 of thequartz crystal device 500 comprises a mid-section portion in which eachof the first and second tines 514, 516 comprises a mesa structure formedon or as part of one or both of opposing main surfaces on the first andsecond sides 518, 520. In the mid-section, the first tine 514 comprisesa first side on which a vertically protruding first line structure 514Ais formed as part of a first mesa structure, and a second side oppositethe first side on which a vertically protruding second line structure514B is formed as part of a second mesa structure. The first and secondline structures 514A, 514B extend in the lengthwise direction of thefirst and second tines 514, 516, e.g., the x-direction. On one end, thefirst and second line structures 514A, 514B terminate adjacent torespective terminal end portions of the first and second tines 514, 516,On the other end, the first and second line structures 514A, 514Bterminate adjacent to connected end portions of the first and secondtines 514, 516, or to the base 512, The first and second line structures514A, 514B laterally divide the first and second (left and right) sidesof the first tine 514 into first and second recessed portions 514C, 514Dseparated in a widthwise direction, e.g., the y-direction. In a similarmanner, the second tine 516 comprises a first side on which a verticallyprotruding first line structure 516A is formed and a second sideopposite the first side on which a vertically protruding second linestructure 516B is formed. The first and second line structures 516A,516B extend in the lengthwise direction of the first and second tines514, 516, e.g., the x-direction, and laterally divide the first andsecond (left and right) sides of the second tine 516 into first andsecond recessed portions 516C, 516D separated in a widthwise direction,e.g., the y-direction.

In the illustrated embodiment, the top surfaces of the line structures514A, 514B, 516A, 516B are coplanar with adjacent base 512 and the topportions of the respective tines. However, embodiments are not solimited and in other implementations, the top surfaces of the linestructures 514A, 514B, 516A, 516B may be higher or lower relative to theadjacent base 512 and the top portions of the respective tines.

In the illustrated embodiment, each of the first and second linestructures 514A, 516B of the first tine 514 and the first and secondline structures 516A, 516B of the second tine 516 forms a mesa structurehaving sidewalls that are generally perpendicular with respectiveabutting recessed portions. However, embodiments are not so limited, andin some other embodiments, the one or both sidewalls may form anglesgreater or less than 90°. For example, the one or both sidewalls mayform 40-50°, 50-60°, 60-70°, 70-80°, 80-90° or an angle in a rangeformed by any of these values. In addition, when the sidewalls aretapered, the line structures 514A, 514B, 516A, 516B may or may not havea top surface. Accordingly, in some embodiments, the line structureshave a trapezoidal or triangular cross sectional shapes.

Referring to FIGS. 5A/5B and 5E, the base 512 of the quartz crystaldevice 500 generally has a rectangular shape in a cross sectional view.As illustrated in FIG. 5E, the main surfaces of the base 512 on firstand second sides 518, 520 of the quartz crystal device 500 can begenerally parallel and opposing planar surfaces that are connected byside surfaces of the base 512.

Various portions of the quartz crystal device 500 have surfaces havingformed thereon electrode patterns that are collectively configured tovibrate the tines of the fork-shaped quartz crystal device 500 in atorsional mode. The electrode patterns include a first electrode pattern524 of a first polarity, e.g., one of a negative or positive electrodepattern, and a second electrode pattern 528 of a second polarity, e.g.,the other of the negative or positive electrode pattern.

Referring to the first main (top) surface of the fork-shaped quartzcrystal device 500 illustrated in FIG. 5A, the first (e.g., negative)electrode pattern 524 formed on the top surface includes first to fourthportions 524A-524D, and the second (e.g., positive) electrode pattern528 formed on the top surface includes first to fourth portions528A-528D. The first electrode pattern 524 includes a first portion 524Acovering a first (right) side of the base 512 and extends upwardtherefrom in the x-direction in the form of the second thin stripportion 524B. The second thin strip portion 524B extends along a rightor outer edge portion of the second tine 516, and terminates adjacent tothe third portion 528C of the second electrode pattern 528 formed on theterminal end portion of the second tine 516. The first electrode pattern524 additionally includes the third portion 524C formed on the terminalend portion of the first tine 514, extends downward therefrom in thex-direction in the form of the fourth thin strip portion 524D along aleft or outer edge portion of the first tine 514, and terminatesadjacent to the first portion 528A of the second electrode pattern 528formed on the second (left) side of the base 512.

Still referring to the plan view illustrated in FIG. 5A, the secondelectrode pattern 528 formed on the top surface includes the firstportion 528A covering a second (left side) of the base 512 and extendingupward therefrom in the x-direction and forking or splitting into thesecond thin strip portion 528B formed and extending upward along a leftor inner edge portion of the second tine 516, and a fourth thin stripportion 528D formed along and extending upward along a right or inneredge portion of the first tine 514. The fourth thin strip portion 528Dterminates adjacent to the third portion 524C of the first electrodepattern 524 formed on the terminal end of the first tine 514. The secondthin strip portion 528B extends to connect to the third portion 528C ofthe second electrode pattern 528 formed on the terminal end portion ofthe second tine 516.

Referring to the second main (bottom) surface of the quartz crystaldevice 500 illustrated in FIG. 5B, the quartz crystal device 500 hasformed thereon various portions of a first electrode pattern 524′ of thefirst polarity and the second electrode pattern 528′ of the secondpolarity formed thereon. The combined pattern of the first and secondelectrode patterns 524′, 528′ formed on the bottom side 520 maygenerally be shaped similarly as the combined pattern of the first andsecond electrode patterns 524, 528 formed on the front side 518 asdescribed above, except that their polarities are interchanged. Thefirst (e.g., negative) electrode pattern 524′ formed on the bottomsurface includes first to fourth portions 524A′-524D′, and the second(e.g., positive) electrode pattern 528′ formed on the bottom surfaceincludes first to fourth portions 528A′-528D′. The second electrodepattern 528′ includes the first portion 528A′ covering a first (rightside) of the base 512 portion and extends upward therefrom in thex-direction in the form of the second thin strip portion 528B′ along aright or outer edge portion of the first tine 514, and terminatesadjacent to the third portion 524C′ of the first electrode pattern 524′formed on the terminal end portion of the first tine 514. The secondelectrode pattern 528′ additionally includes the third portion 528C′formed on the terminal end portion of the second tine 516, extendsdownward therefrom in the x-direction in the form of the fourth thinstrip portion 528D′ along a left or outer edge portion of the secondtine 516, and terminates adjacent to the first portion 524A′ of thefirst electrode pattern 524′ formed on the second (left) side of thebase 512 portion when viewing the rear side 520.

Additionally referring to the rear side 520, the first electrode pattern524′ formed on the bottom surface includes the first portion 524A′covering a second (left side) of the base 512 portion and extends upwardtherefrom in the x-direction and forks or splits into the second thinstrip portion 524B′ formed and extending upward along a left or inneredge portion of the first tine 514, and a fourth thin strip portion524D′ formed along and extending upward along a right or inner edgeportion of the second tine 516. The fourth thin strip portion 524D′terminates adjacent to the third portion 528C′ of the second electrodepattern 528′ formed on the terminal end of the second tine 516. Thesecond thin strip portion 524B′ extends to connect to the third portion524C′ of the first electrode pattern 524′ formed on the terminal endportion of the first tine 514.

As described above, the fork-shaped torsional mode quartz crystal device500 includes various portions of the first electrode pattern 524 on thefirst side 518 and the first electrode pattern 524′ on the second side520 that are connected to each other. Similarly, various portions of thesecond electrode pattern 528 on the first side 518 and the secondelectrode pattern 528′ on the second side 520 are connected to eachother. The resulting relative positions of different portions of thefirst electrode patterns 524, 524′ and the second electrode patterns528, 528′ are further described below with respect to FIGS. 5C-5E.

FIG. 5C illustrates a cross-sectional view of the fork-shaped quartzcrystal device 500 including a mesa structure, though the section B-B orthrough terminal end portions of the first and second tines 514, 516. Asdescribed above with respect to FIGS. 5A and 5B, the terminal portion ofthe first tine 514 has formed on the first and second sides 518, 520 thethird portion 524C of the first electrode pattern 524 and the thirdportion 524C′ of the first electrode pattern 524′, respectively. Thethird portions 524C and 524C′ are connected by side portions 524C″formed on left and right side surfaces of the first tine 514. Inaddition, the terminal portion of the second tine 516 has formed on thefirst and second sides 518, 520 the third portion 528C of the secondelectrode pattern 528 and the third portion 528C′ of the secondelectrode pattern 528′, respectively. The third portions 528C and 528C′are connected by side portions 528C″ formed on left and right sidesurfaces of the second tine 514. Thus configured, the terminal end ofportion the first tine 514 is wrapped or surrounded by the firstelectrode pattern having the first polarity on top, bottom and sidesurfaces thereof, and the terminal end portion of the second tine 516 issurrounded by the second electrode pattern having the second polarity ontop bottom and side surfaces thereof.

FIG. 5D illustrates a cross-sectional view of the fork-shaped quartzcrystal device 500 comprising a mesa structure through the section C-C(FIG. 5A) at midsections the first and second tines 514, 516. Asdescribed above, each of the first and second tines 514, 516 comprises amesa structure formed on one or both of the first and second sides 518,520. Accordingly, the quartz crystal device 500 comprises electrodepatterns that are formed synergistically with respect to the mesastructures, including the first and second line structures 514A, 514Bformed on the first and second sides 518, 520 of the first tine 514 andthe first and second line structures 516A, 516B formed on the first andsecond sides 518, 520 of the second tine 516.

Referring to FIG. 5D, the first tine 514 has a first main surface on thefirst side 518 having formed thereon the fourth strip portion 524D ofthe first electrode pattern 524 on the outer edge portion thereof, andthe fourth strip portion 528D of the second electrode pattern 528 on theinner edge portion thereof. The first tine 514 additionally has a secondmain surface on the second side 520 having formed thereon the secondstrip portion 524B′ of the first electrode pattern 524′ on the inneredge portion thereof, and the second strip portion 528B′ of the secondelectrode pattern 528′ formed on the outer edge portion thereof. Thusconfigured, the first and second main surfaces of the first tine 514comprises a mesa structure including the first and second linestructures 514A, 514B, respectively, which defines the topography of theelectrode patterns formed thereon. For example, the fourth strip portion524D of the first electrode pattern 524 comprises a portion, e.g., avertical portion, that covers at least a portion of a first (left)sidewall of the first line structure 514A and a portion, e.g., ahorizontal portion, that extends to cover at least a portion of a first(upper) recessed surface of the first recessed portion 514C abutting thefirst sidewall of the first line structure 514A. Similarly, the fourthstrip portion 528D of the second electrode pattern 528 comprises aportion, e.g., a vertical portion, that covers at least a portion of asecond (right) sidewall of the first line structure 514A and a portion,e.g., a horizontal portion, that extends to cover at least a portion ofa first (upper) recessed surface of the second recessed portion 514Dabutting the second sidewall of the first line structure 514A. In asimilar manner as the first side 518, the second side of the first tine514 has formed thereon the fourth strip portion 528B′ of the secondelectrode pattern 528′ comprising a portion, e.g., a vertical portion,that covers at least a portion of a first (left) sidewall of the secondline structure 514B and a portion, e.g., a horizontal portion, thatextends to cover at least a portion of a second (lower) recessed surfaceof the first recessed portion 514C abutting the first sidewall of thesecond line structure 514B. Similarly, the second strip portion 524B′ ofthe first electrode pattern 524′ comprises a portion, e.g., a verticalportion, that covers at least a portion of a second (right) sidewall ofthe second line structure 514B and a portion, e.g., a horizontalportion, that extends to cover at least a portion of a second (lower)recessed surface of the second recessed portion 514D abutting the secondsidewall of the second line structure 514B. Thus formed, each of thefirst electrode portions 524D, 523B′ and second electrode portions528B′, 528D have surfaces facing each other in a widthwise direction(y-direction) and configured such that, when a bias is applied betweenthe first and second electrodes 524/524′, 528/528′, the fork-shapedquartz crystal device 500 vibrates in a torsional mode in which each ofthe tines 514, 516 twists about the x-axis.

Still referring to FIG. 5D, the cross-sectional view through the sectionC-C shows the second tine 516 having an analogous structure as the firsttine 514, where the first line structure 516A, the second line structure516B, the first recessed structure 516C and the second recessedstructure 516D are formed in an analogous manner as the correspondingtopography including the first line structure 514A, the second linestructure 514B, the first recessed structure 514C and the secondrecessed structure 514D of the first tine 514, respectively. Inaddition, the second strip portion 528B of the second electrode pattern528, the second strip portion 524B of the first electrode pattern 524,the fourth strip portion 524D′ of the first electrode pattern 524′ andthe fourth strip portion 528D′ of the second electrode pattern 528′ areformed in an analogous manner relative the underlying topography as thefourth strip portion 524D of the first electrode pattern 524, the fourthstrip portion 528D of the second electrode pattern 528, the second stripportion 528B′ of the second electrode pattern 528′ and the second stripportion 524B′ of the first electrode pattern 524′, respectively, thatare formed on the first tine 514.

FIG. 5E illustrates a cross-sectional view of the quartz crystal device500 though the section D-D (FIG. 5A) at the terminal end portion of thebase 512. As described above with respect to FIGS. 5A and 5B, theterminal end portion of the base 512 has formed on the first side 518the first portion 524A of the first electrode pattern 524 on the rightside and the first portion 528A of the second electrode pattern 528 onthe left side. The terminal portion of the base 512 additionally hasformed on the second side 520 the first portion 524A′ of the firstelectrode pattern 524′ on the right side and the first portion 528A′ ofthe second electrode pattern 528′ on the left side. The first portions524A and 524A′ of the first electrode patterns 524 and 524′,respectively, are connected by a side portion 524A″ formed on right sideof the base 512. The first portions 528A and 528A′ of the secondelectrode patterns 528 and 528′, respectively, are connected by a sideportion 528A″ formed on left side of the base 512. As configured, thefirst (e.g., negative) electrode pattern 524/524′ partly surrounds thebase 512 at the right side, and the second (e.g., positive) electrodepattern 528/528′ partly surrounds the base 512 at the left side.

In operation, electrical pulses having a first (e.g., one of negative orpositive) polarity may be applied to the first electrode patterns 524,524′ (including the second and fourth strip portions 524B, 524D on thefront side 518 of the second and first tines 516, 514, respectively, andthe second and fourth strip portions 524B′, 524D′ on the back side 520of the first and second tines 516, 514, respectively, as illustrated inFIG. 5D). On the other hand, electrical pulses having a second (e.g.,the other of negative or positive) polarity may be applied to the secondelectrode patterns 528, 528′ (including the second and fourth stripportions 528B, 528D on the front side 518 of the second and first tines516, 514, respectively, and to the second and fourth strip portions528B′, 528D′ on the back side 520 of the first and second tines 514,516, respectively, as illustrated in FIG. 5D). While embodiments are notso limited, the portions of the first electrode patterns 524, 524′ maybe at the same potential, and the portions of the second electrodepatterns 528, 528′ may be at the same potential. In addition, pulseshaving the first and second polarities may be applied to the quartzcrystal device 500 simultaneously.

When the first and second electrode patterns 524/524′, 528/528′ arebiased as described herein, the resulting electric field generallyfollows, e.g., on average, the paths indicated by the arrows in FIG. 5D.Advantageously, compared to the curvilinear electric field pathsfollowed by the respective electrodes illustrated for the quartz crystaldevice 100 described above with respect to FIGS. 1A and 1B, the electricfield paths include direct horizontal paths between the verticalportions of adjacently disposed electrodes of opposite polarities. Forexample, the electric field paths include a horizontal path from thevertical portions of the second strip portion 528B on the left sidewallof the first line structure 516A of the second tine 516, the fourthstrip portion 528D on the right sidewall of the first line structure514A of the first tine 514, the second strip portion 528B′ on the leftsidewall of the second line structure 514B of the first tine 514 and thefourth strip portion 528D′ on right sidewall of the second linestructure 516B of the second tine 516, to facing vertical portions ofthe second strip portion 524B on the right sidewall of the first linestructure 516A of the second tine 516, the fourth strip portion 524D onthe left sidewall of the first line structure 514A of the first tine514, the second strip portion 524B′ on the right sidewall of the secondline structure 514B of the first tine 514 and the fourth strip portion524D′ on the left sidewall of the second line structure 516B of thesecond tine 516, respectively. It will be appreciated that the electricfield paths indicated by the arrows between the vertical electrodeportions are generally horizontal and in directions that are orthogonalto the electrode surfaces, In addition, the distance traversed by theelectric field paths, e.g., the thicknesses of the first and second linestructures 514A, 514B of the first tine 514 and the first and secondline structures 516A, 516B of the second tine 516, are substantiallysmaller than the corresponding paths traversed by the correspondingelectric field lines described above with respect to FIG. 1B.

Advantageously, the resulting electric field strength is relativelystronger for a given voltage and/or about the same for a lower voltage,thereby enabling more efficient vibration by twisting the first andsecond tines 514, 516, or torsionally vibrating the fork-shaped quartzcrystal device 500. Thus, relatively lower power may be dissipated intorsionally vibrating the quartz crystal device 500 compared to quartzcrystal devices that are configured differently, e.g., the quartzcrystal devices that do not have the line structures protruding on oneor both sides of the tines. In addition, because relatively smallervolume of the quartz substrate is twisted in operation, the inventorshave recognized that the mesa structures can substantially reduce themotional resistance (R₁), thereby further reducing the energy consumedin operation and increasing the quality factor (Q). As configured, theconfiguration of the quartz crystal device 500 can be particularlyadapted for lower power and higher precision applications.

FIGS. 6A-6C schematically illustrate perspective views of thefork-shaped torsional mode quartz crystal device 500 described abovewith respect to FIGS. 5A-5E. FIG. 6A illustrates the fork-shaped quartzcrystal device 500 in a rest state, while FIG. 6C illustrates the quartzcrystal device 500 under a simulated bias conditions in which the tinesare torsionally twisted. FIG. 6B schematically illustrates across-sectional view of the tines including the electrodes. When thefirst electrode patterns 524, 524′ and the second electrode patterns528, 528′ are subjected to negative and positive voltages, respectively,as described above, such that the electric field limes compriserelatively strong horizontal vector components between vertical portionsof the second electrode patterns 528, 528′ and the correspondingvertical portions of the first electrode patterns 524, 524′, the firstand second tines 514, 516 twist about the x-axis extending in thelengthwise direction with increased efficiency, as illustrated in FIG.6C. When the first and second electrode patterns 524/524′, 528/528′ aresubjected to pulsed negative and positive voltages, the fork-shapedquartz crystal device 500 can toggle between the rest state illustratedin FIG. 6A and the deformed or twisted state illustrated in FIG. 6C.

The piezo-electrical effect in quartz can be utilized in differentvibrational modes based the way the crystal wafers or blanks are cut outof the raw bulk crystal in regards of their orientation to the atomiclattice. Some commonly used vibrational modes include, e.g., flexural,extensional, face shear and thickness shear modes, to name a few. Inorder to utilize the desired vibration mode, the quartz crystals are cutin a certain angle with respect to the quartz lattice. FIG. 7schematically illustrates different crystal orientations for differenttypes of quartz crystal devices including a fork-shaped torsional modequartz crystal device, according to embodiments. Commonly used cuts ofquartz crystal include, e.g., X-cut, Z-cut, NT-cut, AT-cut, BT-cut andSC-cut, to name a few. Referring to FIG. 7 , according to variousembodiments disclosed herein, the fork-shaped quartz crystal devicesconfigured for torsional vibration are fabricated from a Z-cut quartz.The quartz crystals for torsional vibration have surface normaldirections of main surfaces that are rotated at a tilt angle θ of about−50 degrees to +50 degrees, about −40 degrees to +40 degrees, or about−30 degrees to +30 degrees relative to a X-axis. In addition, thelengths of the tines of the quartz crystal devices extend in the X-axisof the quartz crystal. This is notably in contrast with tuning forkquartz crystal devices configured for flexural vibrations, in which thelengths of the tines extend in the Y-axis of a quartz crystal from whichthe devices are fabricated. For example, referring back to FIGS. 5A-5E,the top surfaces of the first and second line structures 514A, 514B ofthe first tine 514 the top surfaces of the first and second linestructures 516A, 516B of the second tine 516 are rotated at the θrelative to the X-axis.

In the following, various physical characteristics of the fork-shapedquartz crystal devices according to embodiments are described.

One application for quartz crystal devices described herein is atemperature sensor. The quartz crystal devices are particularly suitablefor a temperature sensor application because the frequency of the quartzcrystal devices described herein have a substantially linearrelationship with temperature. The relationship between the frequency ofoscillation of a quartz crystal device and temperature may berepresented by the following approximate polynomial expression:

(f(T)−f(T ₀))/f(T ₀)=α(T−T ₀)+β(T−T ₀)²+γ(T−T ₀)³,  [3]

where T₀ is a reference temperature, e.g., 25° C., f(T₀) is thefrequency at the T₀, f(T) is the frequency of the crystal subjected tothe temperature T, and α, β and γ are coefficients that are independentof temperature. For temperature sensor applications, it is desirablethat the temperature dependence of the f(T) be as linear as possiblebecause it allows for direct and accurate conversion between temperatureand frequency in a numerical or quasi-numerical manner. Thus, bymeasuring the f(T), which can be performed with a high degree ofresolution, a correspondingly accurate temperature can be calculatedbased on the linear relationship. For a high degree of linearity of thef(T), the non-linear coefficients β and γ should be as small as possiblerelative to the linear coefficient a. FIG. 8A illustrates a lineartemperature coefficient α as a function of an angle θ for a fork-shapedtorsional mode quartz crystal device, according to embodiments.According to various embodiments, α can have a value of about1×10⁻⁶-1×10⁻⁵° C.⁻¹, 1×10⁻⁵-2×10⁻⁵° C.⁻¹, 2×10⁻⁵-3×10⁻⁵° C.⁻¹,3×10⁻⁵-4×10⁻⁵° C.⁻¹, 4×10⁻⁵-5×10⁻⁵° C.⁻¹, or a value in a range definedby any of these values, for instance 1×10⁻⁵-3×10⁻⁵° C.⁻¹, when thequartz crystal device is configured according to any of configurationsdescried herein. Typical experimental and finite element analysis(FEA)-simulated α, β and γ values for one example configuration of thefork-shaped quartz crystal device similar to that described in FIGS.5A-5E are shown in TABLE 1 below.

TABLE 1 Experimental Data FEA Simulation α,/° C. 3.44E−05 3.61E−05 β,/°C.² 1.93E−08 2.29E−08 γ,/° C.³ 2.82E−11 5.14E−11

According to various embodiments described herein, the quartz crystaldevices can be operated at a frequency in a range between about 100 kHzand 500 kHz. Example frequencies that can be used to operate the quartzcrystal device include, e.g., 172.0 kHz, 190.5 kHz, 262.144 kHz, 300.0kHz, 325.0 kHz, and 350.0 kHz, to name a few.

FIGS. 8B and 8C illustrates the linearity of the f(T) for examplefork-shaped quartz crystal devices according to embodiments. FIG. 8Billustrates a frequency versus temperature curve at an angle of tilt of−30° relative to the X-axis of a quartz crystal for a fork-shapedtorsional mode quartz crystal device having a mesa structure accordingto embodiments. FIG. 8C illustrates a frequency versus temperature curveat an angle of tilt of 30° relative to the X-axis of a quartz crystalfor a fork-shaped torsional mode quartz crystal device having a mesastructure according to embodiments. The linearity coefficient α for theexamples illustrated in FIGS. 8B and 8C were 3.9×10⁻⁵° C.⁻¹ and 9×10⁻⁶°C.⁻¹, respectively.

FIG. 9 illustrates a frequency versus thickness curves for fork-shapedtorsional mode quartz crystal devices with and without a mesa structure.Both structures demonstrate a substantially linear relationship betweenthe thickness t or t₁ and the resonance frequency. In addition,fork-shaped torsional mode quartz crystal devices with a mesa structuredemonstrate a substantially linear relationship between the thickness t₁of the recessed regions of the tines and the resonance frequency.

As described above with respect to Eq. [1], the motional resistance(R₁), the motional capacitance (C₁) and the quality factor (Q) arefigures of merit for quartz crystal devices. The inventors havediscovered that, by forming the mesa structures on the tines of thefork-shaped torsional quartz crystal devices as described herein, theR₁, C₁ and Q can be advantageously engineered for improved torsionalvibration compared to fork-shaped torsional quartz crystal devices thatdo not have the mesa structures formed on the tines. FIGS. 10A-10Cillustrate qualitatively different frequency or thickness dependenciesof the R₁, C₁ and Q between the quartz crystal devices configured fortorsional vibration without (e.g., FIGS. 1A and 1B) and with (FIGS.5A-5E) line or mesa structures formed on the tines of the fork-shapedquartz crystal devices.

FIG. 10A is a graph illustrating the R₁ as a function of frequency forfork-shaped torsional mode quartz crystal devices with and without amesa structure. As illustrated, without the line or mesa structuresformed on the tines, the R₁ of the fork-shaped torsional quartz crystaldevice generally decreases with increasing frequency at least within theillustrated frequency range. In contrast, the R₁ of the fork-shapedtorsional quartz crystal device having the line or mesa structuresformed on the tines generally increases with increasing frequency atleast within the illustrated frequency range.

FIG. 10B is a graph illustrating the C₁ as a function of frequency forfork-shaped torsional mode quartz crystal devices with and without amesa structure. As illustrated, without the line or mesa structuresformed on the tines, the C₁ of the fork-shaped torsional quartz crystaldevice generally increases with increasing frequency at least within theillustrated frequency range. In contrast, the C₁ of the fork-shapedtorsional quartz crystal device having the line or mesa structuresformed on the tines generally decreases with increasing frequency atleast within the illustrated frequency range.

FIG. 10C is a graph illustrating quality factor (Q) as a function offrequency for fork-shaped torsional mode quartz crystal devices with andwithout a mesa structure. From FIGS. 10A and 10B, it will be appreciatedthat, while the R₁ is generally lower and the C₁ is generally higher forfork-shaped torsional quart crystal devices with line or mesa structureson the tines compared to those without the line or mesa structures onthe tines, the decrease in magnitude of the R₁ is greater than theincrease in magnitude of the C₁. In sum, as illustrated, the fork-shapedtorsional quartz crystal devices with line or mesa structuresadvantageously have significantly higher value of the Q at least withinthe illustrated frequency range.

According to various embodiments, fork-shaped torsional quartz crystaldevices with line or mesa structures have an R₁ of 1-10 kΩ, 10-20 kΩ,20-30 kΩ, 30-40 kΩ or a value in a range defined by any of these values,a C₁ of 0.1-0.2 fF, 0.2-0.3 fF, 0.3-0.4 fF, 0.4-0.5 fF, 0.5-0.6 fF,0.6-0.7 fF, 0.7-0.8 fF, 0.8-0.9 fF, 0.9-1.0 fF, 1.0-1.1 fF, 1.1-1.2 fF,1.2-1.3 fF or a value in a range defined by any of these values orgreater, and a Q of 10,000-20,000, 20,000-50,000, 50,000-200,000,200,000-400,000, 400,000-600,000, 600,000-800,000, 800,000-1,000,000, ora value in a range defined by any of these values, for a frequency rangeincluding at least 172.0 kHz to 350.0 kHz, according to embodiments.

Advantageously, the shape of the fork-shaped torsional mode quartzcrystal devices having mesa or line structures formed on the tines offera greater number of physical parameters that can be optimized for thedesired performance. For example, the physical parameters that can beoptimized include the overall thickness of the quartz crystal device,the height of the line or mesa structure, the width of the line or mesastructure and the length of the line or mesa structure, to name a few.The technical effects of optimizing these parameters are describedbelow.

FIG. 11 is a graph illustrating the frequency and the motionalcapacitance (C₁) as a function of the height of the line structure orthe mesa thickness for fork-shaped torsional mode quartz crystal devicescomprising a mesa structure, according to embodiments. As illustrated,the frequency and the C₁ can vary inversely as a function of the heightof the line structure or the mesa thickness

FIG. 12A is a graph illustrating the motional resistance (R₁) and themotional capacitance (C₁) as a function of a ratio (t₁/t) between athickness (t₁) of the recessed region of a tine and a thickness (t) ofthe line region of the tine of the fork-shaped torsional mode quartzcrystal devices, according to embodiments. FIG. 12B is a graphillustrating the frequency and the quality factor (Q) as a function ofthe t₁/t for the fork-shaped torsional mode quartz crystal devices. Asillustrated, the R₁ can be lowered at a faster rate compared to the rateof increase of the C₁ by decreasing the t₁/t, such that the Q canadvantageously be significantly increased. According to variousembodiments, the t₁/t can be about 0.01-0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8,0.8-0.99, or have a value in a range defined by any of these values.

FIG. 13A is a graph illustrating the motional resistance (R₁) and themotional capacitance (C₁) as a function of a ratio (W₁/W) between awidth (W₁) of a line region and an overall width (W) of the tines offork-shaped torsional mode quartz crystal devices comprising a mesastructure, according to embodiments. FIG. 13B is a graph illustratingthe frequency and the quality factor (Q) as a function of the W₁/W forthe fork-shaped torsional mode quartz crystal devices comprising a mesastructure. As illustrated, the R₁ can be lowered at a faster ratecompared to the rate of increase of the C₁ by decreasing the W₁/W, suchthat the Q can advantageously be significantly increased. According tovarious embodiments, the W₁/W can be about 0.01-0.2, 0.2-0.4, 0.4-0.6,0.6-0.8, 0.8-0.99, or have a value in a range defined by any of thesevalues.

FIG. 14A is a graph illustrating the motional resistance (R₁) and themotional capacitance (C₁) as a function of a ratio (L₁/L) between alength (L₁) of the tip regions of the tines excluding the line regionsand a length (L) of the tines including the tip regions and the lineregions for fork-shaped torsional mode quartz crystal devices comprisinga mesa structure, according to embodiments. FIG. 14B is a graphillustrating the frequency and the quality factor (Q) as a function ofthe L₁/L for the fork-shaped torsional mode quartz crystal devices. Asillustrated, the R₁ can be lowered at a faster rate compared to the rateof increase of the C₁ by decreasing the L₁/L down to about 0.3, suchthat the Q can advantageously be increased. According to variousembodiments, the L₁/L can be about 0.01-0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8,or have a value in a range defined by any of these values.

According to some embodiments, a length (L) of the tines of thefork-shaped torsional mode quartz crystal devices can be about 500-1000μm, 1000-1500 μm, 1500-2000 μm, 2000-2500 μm, 2500-3000 μm, or any valuein a range defined by these values, for instance 1778 μm.

According to some embodiments, a length (L₁) of the tip regions of thetines of the fork-shaped torsional mode quartz crystal devices can beabout 100-300 μm, 300-500 μm, 500-700 μm, 700-900 μm, or any value in arange defined by these values, for instance 508 μm. The L₁ can also bedefined by any of the L₁/L values described above.

According to some embodiments, a length (L_(m)) of the base (e.g., 512,FIG. 5A) of the fork-shaped torsional mode quartz crystal devices can beabout 100-300 μm, 300-500 μm, 500-700 μm, 700-1000 μm, or any value in arange defined by these values, for instance 635 μm.

According to some embodiments, a width (W) of a tine of the fork-shapedtorsional mode quartz crystal devices can be about 100-200 μm, 200-300μm, 300-400 μm, 400-500 μm, or any value in a range defined by thesevalues, for instance 236 μm.

According to some embodiments, a width (W₁) of a line or mesa structureformed on a tine of the fork-shaped torsional mode quartz crystaldevices can be about 1-20 μm, 20-40 μm, 40-60 μm, 60-80 μm, 80-100 μm orany value in a range defined by these values, for instance 50 μm.

According to some embodiments, a thickness (t₁) of a recessed region ofa tine of the fork-shaped torsional mode quartz crystal devices can beabout 40-60 μm, 60-80 μm, 80-100 μm, 100-120 μm, or any value in a rangedefined by these values, for instance 85 μm.

According to some embodiments, a thickness (t) of the fork-shapedtorsional mode quartz crystal devices can be about 60-90 μm, 90-120 μm,120-150 μm, 150-180 μm, or any value in a range defined by these values,for instance 120 μm.

FIG. 15A illustrates experimentally measured frequency and motionalcapacitance (C₁) versus mesa thickness for a fork-shaped torsional modequartz crystal device comprising a mesa structure, according toembodiments. FIG. 15B illustrates experimentally measured linearity ofthe f(T) and the R₁ of fork-shaped torsional mode quartz crystaldevices, according to embodiments. The simulated and measured linearitycoefficients α are in reasonably good agreement, at 3.61×10⁻⁵° C.⁻¹ and3.44×10⁻⁵° C.⁻¹, respectively.

FIG. 16A illustrates a plan-view of a packaged fork-shaped torsionalmode quartz crystal device 1600 packaged in a ceramic package, accordingto some embodiments. FIG. 16B illustrates a cross-sectional view of thepackaged fork-shaped torsional mode quartz crystal device 1600illustrated in FIG. 16A, which includes the fork-shaped torsional modequartz crystal device 500 enclosed, e.g., hermetically sealed, in theceramic package illustrated in FIG. 16A. The fork-shaped torsional modequartz crystal device 500 may be, e.g., any one of the fork-shapedtorsional quartz crystal devices described herein. The ceramic packageincludes a ceramic package substrate 1612 and a lid 1608 for housing thefork-shaped torsional mode quartz crystal device 500 according tovarious embodiments described above.

The ceramic package substrate 1612 comprises a ceramic frame having aplurality walls that form a cavity 1616 configured to house thefork-shaped torsional mode quartz crystal device 500. The ceramicpackage substrate 1612 is configured to provide thermal and electricalcommunication between the fork-shaped torsional mode quartz crystaldevice 500 and the outside world, e.g., a PCB (not shown), through oneor more metallization structures (not shown). One or more mountingpedestals 1620 (FIG. 16B) may be formed inside the cavity 1616 of theceramic package substrate 1620 that are configured for mounting thefork-shaped torsional mode quartz crystal device 500. While not shown,the mounting pedestals 1620 may have formed thereon an innermetallization pad that is electrically connected to an outermetallization pad for providing electrical and thermal communicationbetween the fork-shaped torsional mode quartz crystal device 500 and theoutside world. In the illustrated embodiment, the fork-shaped torsionalmode quartz crystal device 500 is bonded at two points on each of thepedestals 1620. However, embodiments are not so limited and in otherembodiments, the fork-shaped torsional mode quartz crystal device 500may be bonded at one or three or more points.

The fork-shaped torsional mode quartz crystal device 500 may be bondedto the ceramic package substrate 1612 using one or more bonding layers1624 (FIG. 16B), e.g., a conductive paste layer such as a silver epoxylayer or a conductive silicon-based bonding layer. As described above,the fork-shaped torsional mode quartz crystal device 500 has formedthereon one or more electrode patterns, e.g., first electrode patterns524, 524′ (FIG. 5A-5E) and second electrode patterns 528, 528′ (FIGS.5A-5E). The bonding of the fork-shaped torsional mode quartz crystaldevice 500 on the ceramic package substrate 1612, e.g., on the mountingpedestals 1620 may be performed by bonding the electrode pattern formedthereon, mechanically and/or electrically, to a metallization structureformed on the ceramic package substrate 1612, e.g., on the mountingpedestals 1620. For example, the metallization structure of the ceramicpackage substrate 1612 and the electrode pattern on the quartz crystaldevice 500 may comprise gold, such that a bonding layer 1624 formedtherebetween contacts gold on both sides. Referring to FIG. 16B, thefork-shaped torsional mode quartz crystal device 500 may be hermeticallysealed by bonding the lid 1608 on rims of the ceramic package substrate1612 using a substrate bonding layer 1628.

FIG. 17A illustrates a plan-view of a packaged quartz crystal oscillatordevice 1700 comprising a fork-shaped quartz crystal device 500 packagedin a ceramic package, according to some embodiments. FIG. 17Billustrates a cross-sectional view of the packaged quartz crystaloscillator device 1700 illustrated in FIG. 17A, which includes thefork-shaped quartz crystal device 500 enclosed, e.g., hermeticallysealed, in the ceramic package illustrated in FIG. 17A, in a similarmanner as described above with respect to FIGS. 16A and 16B. The ceramicpackage includes a ceramic package substrate 1712 and a lid 1608 forhousing the quartz crystal device 500 according to various embodimentsdescribed above. The fork-shaped quartz crystal device 500 may bepackaged using a two-point bonding method similar to the packaged quartzcrystal device described above with respect to FIGS. 16A-16B, e.g.,using a bonding layer 1624 formed of conductive paste, in a similarmanner as described above with respect to FIGS. 16A and 16B. Inaddition, in the illustrated embodiment, an integrated circuit (IC) die1704 comprising control circuitry for controlling, e.g., providingoscillation signals to, the quartz crystal device 500, is additionallybonded to the ceramic substrate 1712 using a bonding layer 1624. The IC1704 may be electrically connected to the metallization structuresformed in the ceramic package substrate 1712 through one or more wires1716 bonded therebetween. The metallization structures may in turn beelectrically connected the fork-shaped quartz crystal device 500 throughone or more metallization structures formed in the ceramic packagesubstrate 1712. The metallization structures formed in the ceramicpackage substrate 1712 may in turn provide thermal and electricalcommunication between the quartz crystal device 500 and the IC 1704 andthe outside world, e.g., a PCB (not shown).

In some embodiments, the IC die 1704 is disposed at a different verticallevel from the fork-shaped quartz crystal device 500. For example, inthe illustrated embodiment, the IC die 1704 is disposed below thefork-shaped quartz crystal device 500 and laterally overlaps the IC die1704 for compact packaging. However, embodiments are not so limited. Forexample, in other implementations, the fork-shaped quartz crystal device500 may be formed below the IC die 1704. In yet other implementations,the fork-shaped quartz crystal device 500 and the IC die 1704 may belaterally adjacently disposed to each other at similar vertical levels.Advantageously, the fork-shaped quartz crystal device 500 and theintegrated circuit die 1704 can be processed simultaneously, includingco-sintering the bonding layers for bonding the fork-shaped quartzcrystal device 500 ad the IC die 1704.

FIGS. 18A-18C schematically illustrate various views of a fork-shapedtorsional mode quartz crystal device 1800, according to embodiments. Thequartz crystal device 1800 has a front side 518 having a first mainsurface, e.g., a front surface, and a rear side 520 (FIGS. 18B, 18C)opposite the first side having a second main surface, e.g., a rearsurface. FIG. 18A illustrates a first side (e.g., a top side) and asecond side (bottom side) of the fork-shaped quartz crystal device 1800,respectively. FIGS. 18B, 18C illustrate cross-sectional views of thefork-shaped quartz crystal device 1800 taken at cross-sections H-H andI-I, respectively, as illustrated in FIG. 18A. The fork-shaped quartzcrystal device 1800 is similar to corresponding features of thefork-shaped quartz crystal device 500 described above with respect toFIGS. 5A-5E, except for the presence of one or more vibration isolationarms 1804 and 1804, and a detailed description of the similarities maynot be repeated herein for brevity. Referring to FIGS. 18A-18C, unlikethe fork-shaped quartz crystal device 500 described above with respectto FIGS. 5A-5E in which the first and second base portions 512A, 512B ofthe base 512 are coextensive in the width (y) direction, in theillustrated embodiment, the second base portion 512B below the notches532 further extend in both horizontal (x) directions to form a pair ofvibration isolation arms 1804, 1804. When present, the vibrationisolation arms 1804, 1808 can reduce the amount of vibration leakagefrom the first and second tines 514, 516 to the base 512, such that thequartz crystal device 1800 vibrates with increased efficiency and/orwith higher quality factor. Each of the vibration isolation arms 1804,1808 comprises a horizontal portion extending in a first direction,e.g., the y-direction, from the second base portion 512B and a verticalportion that forms a right angle with the horizontal portion and extendsin a second direction different from the first direction, e.g., thex-direction. In the illustrated embodiment, the distal end of thevertical portion is connected to a tip region that may be wider than thevertical portion. Other suitable shapes and configurations of thevibration isolation arms 1804, 1808 are possible. For example, thevibration isolation arms 1804, 1808 may have horizontal portions but notthe vertical portions. In addition, the angle between the horizontal andvertical portions can be any suitable angle. In addition, the tip regioncan have shapes other than the rectangular shape in plan-view asillustrated in FIG. 18A. For example, the tip region can have anypolygonal and curved shapes. In addition, referring to FIG. 18C, whilein the illustrated embodiment, the vibration isolation arms 1804, 1808generally have similar thickness as the first and tines 514, 516,embodiments are not so limited, and the vibration isolation arms 1804,1808 can be thicker or thinner than the first and second tines. Inaddition, while in the illustrated embodiment, the vibration isolationarms 1804, 1808 generally have a rectangular similar thickness as thefirst and tines 514, 516, embodiments are not so limited, and thevibration isolation arms 1804, 1808 can be thicker or thinner than thefirst and second tines. In addition, the tip region can have shapesother than the rectangular shape in cross-sectional view as illustratedin FIG. 18C. For example, the tip region can have any polygonal andcurved shapes.

FIG. 19A illustrates a plan-view of a fork-shaped quartz crystaloscillator device 1900 packaged in a ceramic package substrate,according to some embodiments. FIG. 19B illustrates a cross-sectionalview of the packaged quartz crystal oscillator device 1900 illustratedin FIG. 19A, which includes the fork-shaped quartz crystal device 1900enclosed, e.g., hermetically sealed, in the ceramic package illustratedin FIG. 19A, in a similar manner as described above with respect toFIGS. 16A and 16B. The packaged quartz crystal oscillator device 1900 issimilar to the packaged quartz crystal oscillator device described abovewith respect to FIGS. 17A-17B, and the similarities may not be repeatedherein for brevity. Unlike the device described above with respect toFIGS. 17A-17B, the fork-shaped quartz crystal device packaged in theceramic package is the fork-shaped torsional mode quartz crystal device1800 described above with respect to FIGS. 18A-18C having one or morevibration isolation arms. The fork-shaped quartz crystal device 1800 theintegrated circuit (IC) die 1704 may be bonded to the ceramic substrate1712 and interconnected to each other and connected to the outside worldin a similar manner as described above with respect to FIGS. 17A-17B.

Aspects of this disclosure can be implemented in various electronicdevices. In particular, applications of the electronic devices include,but are not limited to, high temperature, high reliability and/or highshock and vibration environments, such as oil/gas exploration,geophysical services, avionics, aerospace, military, process control andother harsh industrial applications. However, applications are not solimited and examples of the electronic devices can include, but are notlimited to, consumer electronic products, parts of the consumerelectronic products, electronic test equipment, cellular communicationsinfrastructure such as a base station, etc. Examples of the electronicdevices can include, but are not limited to, a mobile phone such as asmart phone, a wearable computing device such as a smart watch or an earpiece, a telephone, a television, a computer monitor, a computer, amodem, a hand-held computer, a laptop computer, a tablet computer, apersonal digital assistant (PDA), a microwave, a refrigerator, avehicular electronics system such as an automotive electronics system, astereo system, a DVD player, a CD player, a digital music player such asan MP3 player, a radio, a camcorder, a camera such as a digital camera,a portable memory chip, a washer, a dryer, a washer/dryer, peripheraldevice, a clock, etc. Further, the electronic devices can includeunfinished products. Aspects of this disclosure can be particularlyimplemented in various wireless telecommunication technologies in whichhigh power, high frequency bands, improved linearity and/or improvedefficiency are desired, including military and space applications suchas radars, community antenna television (CATV), radar jammers andwireless telecommunication base-stations, to name a few.

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,”“include,” “including” and the like are to be construed in an inclusivesense, as opposed to an exclusive or exhaustive sense; that is to say,in the sense of “including, but not limited to.” The word “coupled”, asgenerally used herein, refers to two or more elements that may be eitherdirectly connected, or connected by way of one or more intermediateelements. Likewise, the word “connected”, as generally used herein,refers to two or more elements that may be either directly connected, orconnected by way of one or more intermediate elements. Additionally, thewords “herein,” “above,” “below,” and words of similar import, when usedin this application, shall refer to this application as a whole and notto any particular portions of this application. Where the contextpermits, words in the above Detailed Description using the singular orplural number may also include the plural or singular number,respectively. The word “or” in reference to a list of two or more items,that word covers all of the following interpretations of the word: anyof the items in the list, all of the items in the list, and anycombination of the items in the list.

Moreover, conditional language used herein, such as, among others,“can,” “could,” “might,” “may,” “e.g.,” “for example,” “such as” and thelike, unless specifically stated otherwise, or otherwise understoodwithin the context as used, is generally intended to convey that certainembodiments include, while other embodiments do not include, certainfeatures, elements and/or states. Thus, such conditional language is notgenerally intended to imply that features, elements and/or states are inany way required for one or more embodiments or whether these features,elements and/or states are included or are to be performed in anyparticular embodiment.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the disclosure. Indeed, the novel apparatus, methods, andsystems described herein may be embodied in a variety of other forms;furthermore, various omissions, substitutions and changes in the form ofthe methods and systems described herein may be made without departingfrom the spirit of the disclosure. For example, while blocks arepresented in a given arrangement, alternative embodiments may performsimilar functionalities with different components and/or circuittopologies, and some blocks may be deleted, moved, added, subdivided,combined, and/or modified. Each of these blocks may be implemented in avariety of different ways. Any suitable combination of the elements andacts of the various embodiments described above can be combined toprovide further embodiments. The various features and processesdescribed above may be implemented independently of one another, or maybe combined in various ways. All possible combinations andsubcombinations of features of this disclosure are intended to fallwithin the scope of this disclosure.

1. (canceled)
 2. A quartz crystal device configured for temperaturesensing, comprising: a quartz crystal comprising first and secondelongate arms laterally extending from a base region in a horizontallengthwise direction of the quartz crystal; and a first electrode and asecond electrode formed on each of upper and lower sides of each of thefirst and second elongate arms and configured to be biased at oppositepolarities, wherein the first and second electrodes formed on a sameside of each of the first and second elongate arms are formed on quartzsurfaces facing away from each other in a widthwise direction crossingthe lengthwise direction.
 3. The quartz crystal device of claim 2,wherein each of the first and second elongate arms has formed on each ofthe upper and lower sides thereof a vertically protruding line structurelaterally elongated in the horizontal lengthwise direction.
 4. Thequartz crystal device of claim 3, wherein the first and secondelectrodes formed on the same side of each of the first and secondelongate arms are separated from each other by a respective one of theline structures such that portions of the first and second electrodesface each other across the respective one of the line structures.
 5. Thequartz crystal device of claim 3, wherein the first and secondelectrodes formed on the same side of each of the first and secondelongate arms are in contact with surfaces of a respective one of theline structures.
 6. The quartz crystal device of claim 2, wherein thequartz crystal device has a substantially linear temperature dependenceof a resonance frequency, wherein the temperature dependence is suchthat a coefficient of a linear temperature-dependent term is about 10-50ppm/° C.
 7. The quartz crystal device of claim 2, wherein the horizontallengthwise direction corresponds to the X-axis of a quartz crystal fromwhich the quartz crystal is fabricated, and wherein the quartz crystaldevice has surface normal directions of main surfaces that are rotatedbetween about −40 degrees and +40 degrees relative to the X-axis.
 8. Thequartz crystal device of claim 2, wherein the quartz crystal device ishermetically sealed in a package substrate having disposed therein anintegrated circuit (IC) die electrically connected to the quartz crystaldevice and bonded to the package substrate.
 9. The quartz crystal deviceof claim 2, wherein: the first and second electrodes formed on one ofthe upper and lower sides of each of the first and second elongate armsare configured to apply a first electric field between the respectivequartz surfaces that face away from each other in the widthwisedirection, and the first and second electrodes formed on the other ofthe upper and lower sides of each of the first and second elongate armsare configured to apply a second electric field between the respectivequartz surfaces that face away from each other in another widthwisedirection.
 10. The quartz crystal device of claim 9, wherein the firstelectric field and the second electric field have major componentsdirected in opposite widthwise directions.
 11. A quartz crystal deviceconfigured for temperatures sensing, comprising: a quartz crystalcomprising first and second elongate arms laterally extending from abase region in a horizontal lengthwise direction of the quartz crystal;and a first electrode and a second electrode formed on upper and lowersides of each of the first and second elongate arms, wherein the firstand second electrodes have vertical portions facing each other in ahorizontal widthwise direction crossing the lengthwise direction andconfigured to be biased at opposite polarities, the vertical portionsextending in a vertical direction crossing the lengthwise and widthwisedirections.
 12. The quartz crystal of claim 10, wherein the quartzcrystal device is configured such that, in response to a voltage appliedbetween the first and second electrodes, a first electric field isformed between the vertical portions of the first and second electrodeson the upper side and a second electric field is formed between thevertical portions of the first and second electrodes on the lower side,wherein the first electric field is different than the second electricfield.
 13. The quartz crystal device of claim 12, wherein the firstelectric field has a major component directed in a first direction andthe second electric field has a major component directed in a seconddirection that is different than the first direction.
 14. The quartzcrystal device of claim 13, wherein the second direction is opposite thefirst direction.
 15. The quartz crystal device of claim 11, wherein eachof the first and second elongate arms has formed on each of the upperand lower sides thereof a vertically protruding line structure laterallyelongated in the horizontal lengthwise direction.
 16. The quartz crystaldevice of claim 11, wherein the quartz crystal device has asubstantially linear temperature dependence of a resonance frequency,wherein the temperature dependence is such that a coefficient of alinear temperature-dependent term is greater than a coefficient of asecond order temperature-dependent term by a factor exceeding
 500. 17.The quartz crystal device of claim 11, wherein the horizontal lengthwisedirection corresponds to the X-axis of a quartz crystal from which thequartz crystal is fabricated, and wherein the quartz crystal device hassurface normal directions of main surfaces that are rotated betweenabout −40 degrees and +40 degrees relative to the X-axis.
 18. The quartzcrystal device of claim 11, wherein the quartz crystal device ishermetically sealed in a package substrate having disposed therein anintegrated circuit (IC) die electrically connected to the quartz crystaldevice and bonded to the package substrate.
 19. A quartz crystal deviceconfigured for temperature sensing, comprising: a quartz crystalcomprising first and second elongate arms laterally extending from abase region in a horizontal lengthwise direction of the quartz crystal,wherein each of the first and second elongate arms has formed on each ofupper and lower sides thereof a vertically protruding line structurelaterally elongated in the horizontal lengthwise direction; and a firstelectrode and a second electrode formed on lower and upper sides of eachof the first and second elongate arms, wherein the first and secondelectrodes on a same one of the upper and lower sides have oppositepolarities and are separated by a respective one of the line structuressuch that portions of the first and second electrodes face each otheracross the respective one of the line structures.
 20. The quartz crystaldevice of claim 19, wherein the portions of the first and secondelectrodes that face each other across the respective one of the linestructures comprise vertical portions.
 21. The quartz crystal device ofclaim 20, wherein: the vertical portion of the first electrode on theupper side of the first elongate arm is in contact with a left side ofthe line structure on the upper side of the first elongate arm, and thevertical portion of the second electrode on the upper side of the firstelongate arm is in contact with a right side of the line structure onthe upper side of the first elongate arm.
 22. The quartz crystal deviceof claim 21, wherein: the vertical portion of the first electrode on theupper side of the second elongate arm is in contact with a right side ofthe line structure on the upper side of the second elongate arm, and thevertical portion of the second electrode on the upper side of the secondelongate arm is in contact with a left side of the line structure on theupper side of the second elongate arm.
 23. The quartz crystal device ofclaim 21, wherein: the vertical portion of the first electrode on thelower side of the first elongate arm is in contact with a right side ofthe line structure on the lower side of the first elongate arm, and thevertical portion of the second electrode on the lower side of the firstelongate arm is in contact with a left side of the line structure on thelower side of the first elongate arm.
 24. The quartz crystal device ofclaim 19, wherein the quartz crystal device has a substantially lineartemperature dependence of a resonance frequency, wherein the temperaturedependence is such that a coefficient of a linear temperature-dependentterm is greater than a coefficient of a second ordertemperature-dependent term by a factor exceeding
 500. 25. The quartzcrystal device of claim 19, wherein the horizontal lengthwise directioncorresponds to the X-axis of a quartz crystal from which the quartzcrystal is fabricated, and wherein the quartz crystal device has surfacenormal directions of main surfaces that are rotated between about −40degrees and +40 degrees relative to the X-axis.
 26. The quartz crystaldevice of claim 19, wherein the quartz crystal device is hermeticallysealed in a package substrate having disposed therein an integratedcircuit (IC) die electrically connected to the quartz crystal device andbonded to the package substrate.